A132164 Row sums of triangle A134141 (S1p(7)).

1, 1, 8, 78, 918, 12846, 209616, 3909228, 81859548, 1897344828, 48135826656, 1325008302696, 39292978029768, 1247949491330088, 42236558731574208, 1516738194700667856, 57573649342673292816, 2302425590703685075728, 96720470167595138898048

Offset: 0

Author

Wolfdieter Lang, Oct 12 2007

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..409

Crossrefs

Cf. A132165 (alternating row sum of A134141), A049428.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1)*(j+5)!/6!*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 01 2017

Mathematica

a[n_]:=a[n]=If[n==0, 1, Sum[Binomial[n - 1, j - 1] (j + 5)!/6! a[n - j], {j, n}]]; Table[a[n], {n, 0, 25}] (* Indranil Ghosh, Aug 02 2017, after Maple code *)

Formula

a(n)= sum(A134141(n,m),m=1..n),n>=1.

E.g.f.: exp((1-(1-x)^6)/(6*(1-x)^6)). Cf. e.g.f. first column of A134141.

From Seiichi Manyama, Jan 18 2025: (Start)

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A005012(k).

a(n) = (1/exp(1/6)) * (-1)^n * n! * Sum_{k>=0} binomial(-6*k,n)/(6^k * k!). (End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 01 2017